t.test(y1,y2,配对= T)是否意味着var.equal = T？

Question

在R中,是否t.test(y1, y2, paired=T)暗示var.equal=T？

我问,因为这将帮助我弄清楚韦尔奇的t检验是否适合配对t检验.

Answer 1

当您使用x和运行配对测试时y,您实际上正在运行单样本测试d=x-y.这意味着只有一个变量d,因此只有一个样本可以得到方差.

所以谈论var.equal配对测试是没有意义的.

您可以看到所有这三个测试都会给出相同的结果.

> set.seed(0)             # Sample data
> x <- rnorm(50, mean=10)
> y <- x+rnorm(50)

> t.test(x,y,paired=T,var.equal=T)

        Paired t-test

data:  x and y
t = -0.1766, df = 49, p-value = 0.8605
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.2649616  0.2221498
sample estimates:
mean of the differences 
            -0.02140593 

> t.test(x,y,paired=T,var.equal=F)

        Paired t-test

data:  x and y
t = -0.1766, df = 49, p-value = 0.8605
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.2649616  0.2221498
sample estimates:
mean of the differences 
            -0.02140593 

> t.test(x-y)

        One Sample t-test

data:  x - y
t = -0.1766, df = 49, p-value = 0.8605
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.2649616  0.2221498
sample estimates:
  mean of x 
-0.02140593

您可以在Wikipedia上查看详细信息.在那里,您看到Welch仅用于未配对的样品.